Protein biology research as we know it would not be possible without the variety of chromatography resins, beads, membranes, plastic surfaces and other solid or porous materials to immobilize proteins and affinity ligands. Because these tools and methods are just a means to an end rather than the primary focus of research, it is easy for investigators to lose sight of the relative molecular, macromolecular and physical scales involved in the processes being used. In certain ways, those of us who communicate about the chemical reactions that form the basis for protein purification and detection are guilty of perpetuating false notions and perceptions relating to scale. For example, the following illustration (Figure 1) is at the same time both very informative concerning the chemical reactions that take place during the immobilization of an antibody and highly misleading regarding the relative dimensions of the components within the reaction.

Figure 1. Diagram of antibody immobilization to beaded agarose resin. This example illustrates the reactions involved in coupling antibodies to Thermo Scientific AminoLink Plus Coupling Resin (Part No. 20501). The resin is aldehyde-activated beaded agarose to which antibodies, other proteins and molecules can be covalently attached through their primary amines. The result of this reaction creates a reusable affinity resin for use in a variety of purification methods.

For the purpose of communicating key features of the immobilization mechanism, such illustrations show the sizes of functional groups and beaded supports compressed or collapsed into one order of magnitude, even though the true molecular sizes of the functional elements actually span nearly six orders of magnitude (Table 1). Figure 2 provides a more accurate representation of the sizes involved when working with macromolecules having diameters in the low nanometer range as compared to porous resins having diameters in the micron range. In this illustration, individual functional groups and atoms cannot even be seen, as they are nearly one hundred times smaller than the macromolecules being immobilized.

†The original industry standard and source for beaded agarose for manufacture of affinity supports used in laboratories was Sepharose™ 4B, 6B, CL4B and CL6B media from GE Healthcare. Several manufacturers now produce equivalent resins.

Figure 2. Diagram of the relative sizes of agarose beads and antibodies (proteins).

In contrast to such diagrams are the actual specifications of ligand loading and binding capacities, which describe the concentration of immobilized ligands or proteins relative to the prepared affinity resins. Typically, these are stated as the mass of ligand coupled (milligrams, mg), or as the concentration of ligand coupled (micromoles, µmol or sometimes even nanomoles, nmol) of ligand per milliliter (mL) of settled agarose resin (Table 2).

Values are product claims or test specifications and are expressed per milliliter of settled beads, as in a packed 1mL affinity column. See the respective product pages for details.

Thermo Scientific Product

Ligand Load

Binding or Coupling Capacity

AminoLink Plus Coupling Resin

Not reported

1 to 20mg of antibody (IgG)

NHS-Activated Agarose

Not reported

>25mg human IgG

SulfoLink Coupling Resin

Not reported

>5mg reduced human IgG

CarboxyLink Immobilization Resin

>16µmol amine

0.5 to 1mg of peptide

HisPur Ni-NTA Agarose

>15µmol nickel

Up to 60mg His-GFP (27kDa)

Pierce Glutathione Agarose

Not reported

>40mg purified GST;
10mg GST-tagged proteins

Pierce Streptavidin Agarose

Not reported

15 to 28µg biotin;
1 to 3mg biotinylated BSA

Pierce Protein A/G Agarose

Not reported

>7mg human IgG

For the researcher who wishes to envision a more accurate picture of the underlying molecular and physical sizes contained in an immobilized affinity resin, it is instructive to calculate how the ligand loading values and binding capacities relate to the number and size of individual molecules. In this article, we present the calculations needed to answer the following sorts of questions:

What is the volume of a single agarose bead?

How many agarose beads are in one milliliter of settled resin?
(What is the number of agarose beads per milliliter of packed resin?)

How many functional groups are there per agarose bead?
(What is the number of functional groups per bead?)

How many antibody or protein molecules are coupled per agarose bead?

How many antibody or protein molecules can bind to one agarose bead?

Results and discussion

Number of agarose beads per milliliter of settled resin

The first step in making the conversion from concentration (e.g., µg ligand per mL of settled beads) to the number of ligand molecules per bead is to determine the number of beads per milliliter of packed resin. It would be ideal to determine this value empirically in a manner similar to the way cells are counted: make a known dilution of a measured volume of settled beads and then count the beads in a sample under a microscope. We were unable to find published results of this type of measurement. Therefore, our approach is to calculate the average bead volume and then use sphere-packing theory as the basis for estimating the number of those beads in one milliliter of resin.

Beaded agarose is a mixture of bead sizes and the beads are neither perfectly spherical nor hard; as such, sphere-packing theory might provide only a rough estimate of the true value for the number of particles in a given volume. However, for our purposes, it is more than adequate.

In other words, assuming 75% packing efficiency, 0.75mL of actual bead volume will settle to form approximately 1mL of bed volume (e.g., 1mL of resin in a column).

Final calculation:

Number of beads per mL:

= 0.75(1 bead/5.236 x 10-7mL)

= 1.432 x 106 beads/mL of bed

= approx. 1.4 million beads per milliliter of resin

Number of functional or reactive groups per agarose bead

Activated resins are manufactured to have 10 to 100µmol of groups per mL of packed resin.

For example, CarboxyLink Resin is manufactured with 16-20µmol amines per mL of packed beads (resin bed)

We will do the calculation for just 1µmol per mL of resin bed (= 1 x 10-6mol).

The number of molecules, then, is equal to the number of moles times Avogadro’s number: (1 x 10-6mol) x (6.02 x 1023) = 6.02 x 1017 molecules per mL of resin bed.

We can safely say that, for typical activations where beads contain perhaps 20 to 40µmol of reactive groups per mL of resin:

There are trillions of active groups per agarose bead

Number of immobilized antibody molecules per agarose bead

Typically, the protein coupling capacities of activated resins are determined empirically with example experiments (often using mouse or rabbit whole IgG). Usually, these coupling capacities are expressed as micrograms or milligrams of protein per milliliter of resin.

For example, experiments indicate that 1mL of AminoLink Plus Coupling Resin (Part No. 20501) can immobilize 4.7mg mouse IgG with 97% efficiency. That translates into an effective coupling yield of 4.5mg IgG per mL of resin.

Let’s simplify and be conservative by doing the calculation for just 1mg of IgG actually coupled per mL of resin bed.

The MW of IgG = 150,000g/mol; therefore, 1mg of IgG = 6.67 x 10-9mol

This mole quantity times Avogadro’s number is equal to 4.01 x 1015 IgG molecules per mL of resin bed.

There is another very important consideration when attempting to properly visualize the process of affinity purification at the scale of individual agarose beads. Agarose beads are not hard, solid, and impervious; rather, they are a highly porous aerogel with mesh-like structures composed of loosely interwoven polysaccharide strands in helical structures. Therefore, ligands and typical protein molecules can diffuse within the matrix and attach and bind throughout the entire volume of an agarose bead. In other words, attachment is not confined to the outer surface area.

Conclusions

Beads of standard 4% or 6% beaded agarose resins (available from many suppliers) range in diameter from 45 to 165µm, which corresponds to approximately 5000 to 50,000 times the globular protein length or width of antibodies and other proteins. Although diagrams of covalent immobilization methods are instructive for describing the chemical basis for coupling reactions, they are misleading with regard to the relative sizes and numbers of functional groups involved. With a few simple calculations, we have made the necessary unit conversions to express example concentration values (activation levels, loading levels, coupling and binding capacities) in terms of the number of molecules per individual agarose bead. Perhaps for most researchers, knowing these values satisfies merely academic curiosity and provides little practical value. However, we suggest that it is generally helpful for scientists to maintain accurate perceptions about the molecular dynamics of laboratory methods.

Summary of results:

In 4% or 6% beaded agarose supports, individual agarose beads have an average spherical bead volume of about half a nanoliter (0.52nL).

In one milliliter (1mL) of settled agarose resin there are approximately 1.5 million individual agarose beads.